Rivalries. We love them. Live for them. Sport thrives on them. That’s why what’s blossoming here in the desert could be great for golf for the next few years to come.

There may be 129 players in the field, but all eyes rest on two: Tiger Woods and Rory McIlroy. They played the first two rounds in the company of World No. 1 Luke Donald, but he was just a distraction. The galleries cared only for Woods-McIlroy.

The parallels between the two men are obvious. Both were child prodigies. Woods appeared on the Mike Douglas Show at age 2. McIlroy wasn’t quite that young when he appeared on the popular Irish Gerry Kelly show, but he was chipping balls into a washing machine on live TV at 9.

Both were winning tournaments and setting record scores against older opposition from the moment they started playing tournaments. This rivalry almost seems ordained.

Although it’s hard to predict the future on the basis of just two rounds of golf, Woods looks like he could make a serious assault on the majors this year. He feels his swing is close to where it was when he was the dominant force in golf.

“I feel like I’m swinging well, and a lot of things Sean (Foley, Woods’ swing instructor) and I have been working on are starting to feel very comfortable. Consequently I’m shooting good scores,” Woods said.

“The club is in a similar position that I had when I was younger. I’m doing it in a slightly different way – better mechanics but a similar position.”

Music to the ears of golf fans everywhere, and backed up by McIlroy.

“He’s definitely got the ball under control,” McIlroy said. “He seems comfortable. He’s only made a couple of bogeys in two days. He’s not making many mistakes, and he’s very consistent. His ball flight looks good. I’m really looking forward to battling over the weekend.”

Of course Woods never would entertain the thought of singling out one man to beat. He’s far more diplomatic than that.

Not McIlroy, though. He’s champing at the bit to take Woods on.

“Everyone knows I grew up idolizing him, so it would be great for me to test myself against him,” McIlroy said.

More music to the ears of fans the world over.

“It’s a great motivation for me. I feel 2012 is going to be an exciting year for me. “

And hopefully for golf. McIlroy might have only the one major – last year’s U.S. Open – but he was born to win the game’s greatest tournaments. The greatest names in the game feel that way.

“Better than Tiger Woods at the same age,” said Mark O’Meara, himself a major winner and Woods’ mentor.

“Rory is by far the best young player I’ve ever played with,” said 2006 U.S. Open champion Geoff Ogilvy.

“The next No. 1,” Ernie Els said.

Graeme McDowell, the 2010 U.S. Open winner and McIlroy’s countryman, thinks the Northern Irishman is the one player in the game today who can make a serious assault on Woods’ record in the majors.

“Will he achieve what Tiger was doing around 2000 and win 14 major championships? Can he be that good? He’s got that potential,” McDowell said.

Let’s hope so. Let’s hope the pair battle it out over the Abu Dhabi fairways for the next two days, and then do it for real in the tournaments that really count: the majors. It would be great for the game of golf.

To paraphrase the closing line of Casablanca, “This could be the start of a beautiful rivalry.”

• • •

Tiger Tracker: Our full, shot-by-shot breakdown of Friday’s round

A day after a bogey-free, 2-under 70, Tiger Woods fired a 3-under 69, picking up five birdies and two bogeys on Friday in Abu Dhabi – the only player to break par in his star grouping of Rory McIlroy and Luke Donald.

Tiger is now within two shots of the HSBC Championship lead heading into the weekend. Thorbjorn Olesen is at 7 under through 36 holes.

We tracked Tiger’s every shot on Friday (while many of you were sleeping). Take a look at what you missed with our Tracker:

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• • •

Hole No. 18, Par 5, 567 yards

Tiger takes driver on the final hole of the day and pulls it left and will have a tough angle for any chance at going for the green in two.

McIlroy puts his drive in the middle of the fairway and is likely the only one in this group that can go for the green.

Tiger tries to muscle his second shot out of the rough, but puts himself in the rough on the right and it will be a difficult approach for the former World No. 1.

Tiger gets the ball out of the rough and onto the green, but will have about 40 feet for birdie. He lags it well, putting it to within two feet for par, which he makes and cards a 3-under 69, the only player in his group to break par. Tiger is two shots off the lead.

McIlroy lands in the rough on the side of the green in two, chips out and past the hole on his third shot and misses a 12-foot birdie putt. McIlroy fired an even-par 72 on Friday and is two shots back of the lead.

Donald burned the edge of the cup on his birdie attempt, but had to settle for a par and an even-par round of 72.

Tiger on the day: 3 under (5 under for tournament; Final)

• • •

Hole No. 17, Par 4, 483 yards

Using driver, Tiger backs off once and then finds another fairway bunker, getting a hard kick off the fairway.

Tiger lifts out of the bunker and onto the back of the green, about 15 feet from the pin. He reads the putt correctly, but finishes two revolutions short and stays at 5 under.

McIlroy makes a good run at birdie, but it comes up short and is at 5 under through 17 holes.

Tiger on the day: 3 under (5 under for tournament; thru 17 holes)

• • •

Hole No. 16, Par 4, 475 yards

With driver off the tee, Tiger tries to use body language to get it to fade back into the fairway, but it stays in the left rough.

McIlroy also finds himself in the left rough, while Donald hooks left and into a fairway bunker.

Tiger uses a vicious swing to get out of the rough and the ball sails on him into a greenside bunker, where he has plenty of green to work with. He gives the bunker shot a good run, but has a bit more work with the putt than he originally intended with about eight feet left for par. He misses and picks up his second bogey of the day, while also slipping back to 5 under.

Dealing with a better lie, McIlroy hits the green. His birdie putt flies by the hole and has a 4-foot comebacker. He makes it to stay at 5 under.

Donald dropped another shot with a miss on a short par putt and is back to even for the day.

Tiger on the day: 3 under (5 under for tournament; thru 16 holes)

• • •

Hole No. 15, Par 3, 177 yards

Tiger takes aim at the flag in the back right and is the only one of the three in that quadrant, sitting about 15 feet from a birdie.

Donald and McIlroy both go after the center of the green, with Donald running slightly off the back and into the first cut of rough.

Tiger drops another birdie in, moving to 4 under on the day and 6 under for the tournament.

Donald nearly chips in and picks up a par, while McIlroy gives it a ride, but settles for a par as well.

Tiger on the day: 4 under (6 under for tournament; thru 15 holes)

• • •

Hole No. 14, Par 4, 490 yards

Tiger pulls his tee shot to the left and will have to deal with the rough on this long par 4.

Donald and McIlroy found the fairway off the tee.

Tiger can’t get all of it from his position and hits it short of the green and into a greenside bunker. The bunker shot heads right at the hole, but doesn’t release enough, leaving Tiger with about four feet for par. He puts it right in the middle of the hole and stays at 5 under.

McIlroy plays a fantastic second shot to within five feet of the cup. His putt is solid and he picks up a birdie to get back to even for the day and 5 under for the tournament.

Donald goes a bit long on his approach shot, running through the green and into the rough. Donald makes bogey after missing a 3-foot par putt.

Tiger on the day: 3 under (5 under for tournament; thru 14 holes)

• • •

Hole No. 13, Par 4, 414 yards

Looking very confident, Tiger pummels a 3-wood down the left side of the fairway at the shorter par 4.

McIlroy matches Tiger, but on the right side. Donald is struggling off the tee, this time hitting the cart path to the right and bouncing into the desert, but is still in play.

Tiger lands his approach in the right-center of the green and will have about 20 feet for a birdie. He isn’t leaving putts short anymore, giving this one a chance, but it slides by and he taps in for a par.

McIlroy follows suit and gets inside of Tiger with his approach, but has a winding putt from right to left. He two-putts for a par.

Donald plays a superb shot from the mess he found himself in, landing it a few feet from the cup to turn disaster into a birdie attempt. And he makes the improbable birdie to move to 3 under.

Tiger on the day: 3 under (5 under for tournament; thru 13 holes)

• • •

Hole No. 12, Par 3, 186 yards

Tiger seems to be getting dialed in, landing this tee shot within four feet of the hole and will be looking at another realistic birdie attempt.

Donald and McIlroy both take aggressive lines as well, with Donald going over the green and into a bunker and McIlroy landing just outside of Tiger’s ball.

Tiger makes the putt for a second-straight birdie and he moves to 5 under for the tournament (3 under on the day).

Hole No. 11, Par 4, 417 yards

Tiger is the only one to find the fairway on No. 11, using 3-wood up the left side.

Donald finds another fairway bunker while McIlroy finds a fairway bunker as well with a 3-wood.

Tiger flies his approach shot right over a greenside bunker and onto the front of the green. He got a bit unlucky that it didn’t take a bigger bounce, but is still looking at 15 feet for birdie. He makes the long attempt for his third birdie of the day and is now 4 under for the tournament.

Donald is able to get inside of Tiger with his second shot, while McIlroy can’t get as much juice on his bunker shot and he comes up short in the long rough in front of the green.

McIlroy goes from trouble to even more trouble, with his third shot bounding through the green and into another greenside bunker, where he powers it out but is looking at 12 feet for bogey. He makes it to limit the damage, but still falls back to 3 under for the tournament (2 over for the day).

Donald two-putts to stay at 1 under for the day.

Tiger on the day: 2 under (4 under for tournament; thru 11 holes)

• • •

Hole No. 10, Par 5, 582 yards

Tiger finds the rough on the left side of the fairway, while Donald and McIlroy pound their drives into the middle of the fairway.

Tiger has to lay up and his third shot simply lands in the middle of the green, leaving a long putt for birdie. He misses it and that leaves him 6-for-7 on par 5s – six pars and one birdie.

McIlroy is able to make it in two, and lands it nearly pin high, leaving himself about 20 feet for eagle. He misses that putt on the left, but taps in from one foot for a birdie to move to 4 under.

Donald also had to lay up, but his approach shot stops around 10 feet from the hole. Donald makes the putt and moves to 2 under.

Tiger on the day: 1 under (3 under for tournament; thru 10 holes)

• • •

Hole No. 9, Par 4, 456 yards

Using 3-wood off the tee, Tiger hits a low-liner that never gets more than 10 feet off the ground and runs through the fairway and into the left rough.

McIlroy also finds the left rough, while Donald is in the middle of the fairway.

Tiger, playing his second shot first for one of the few times over the past two days, comes up short of the green and then plays a nice punch shot up the green that stops three feet from the hole. He slides it in for a par and will make the turn at 1 under for the day and 3 under for the tournament (currently four shots off the pace).

McIlroy flirts with a greenside bunker right next to the hole on his second shot, but it manages to stay up, just off the green. His putt from off the green settles one inch from the cup and he has to settle for par. But it wasn’t really a par, he received a two-stroke penalty for wiping sand from in front of his ball when he wasn’t on the green.

Donald hits the green in regulation and two-putts for another steady par.

Tiger on the day: 1 under (3 under for tournament; thru 9 holes)

• • •

Hole No. 8, Par 5, 597 yards

Yelling at his ball to “bite, bite, bite” in the air, Tiger gets his way and the tee ball settles on the right side of the fairway.

McIlroy cleanly hits a fairway for one of the first times on Friday, while Donald hooks his drive badly and finds trouble in the sand and palm trees.

Tiger takes a whack at his second shot, but it comes up short and lands in the greenside bunker right in front of the pin. He plays a creative bunker shot, hitting the fringe and watching the ball trickle onto the green and five feet from the hole. And he drains the birdie putt to move into red numbers for the round.

McIlroy also tries to make it in two, and hooks it into a greenside bunker on the left of the green. Crouched down significantly, McIlroy hits a low, running bunker shot back across the green and it stops about four feet from the hole. McIlroy also makes the birdie putt and is back to even par for the day.

Donald lays up and then hits a fantastic third shot to give himself eight feet for birdie. Donald has to putt the ball gingerly down the hill and it misses on the left and he picks up another par.

Tiger on the day: 1 under (3 under for tournament; thru 8 holes)

• • •

Hole No. 7, Par 3, 200 yards

With the pin tucked in the back right, Tiger takes aim and flies over the flag and about 20 feet behind the hole.

McIlroy hits a nice shot to within 10 feet, while Donald comes up short and misses the green in the front.

Tiger gives it a good run, but his birdie putt slides by on the right and he settles for par.

McIlroy two-putts for a par and Donald gets up-and-down from the greenside bunker for par.

Tiger on the day: Even par (2 under for tournament; thru 7 holes)

• • •

Hole No. 6, Par 4, 469 yards

Using a fairway wood, Tiger smacks his tee shot into the middle of the fairway, with Donald following suit. McIlroy pushes his drive into the first cut of rough.

Posing after he hit it, Tiger misses his second green in regulation on the day, landing in a greenside bunker. With not much green to work with, Tiger spends time studying the lie in the sand. While the shot comes to rest a reasonable five feet away, Tiger look disgusted and shows the first sign of real emotion over the first two days. He makes the putt and remains at 2 under for the tournament.

Donald manages to hit the green while McIlroy is just on the fringe, both looking at around 20 feet for birdie. Both players two-putt to save par.

Tiger on the day: Even par (2 under for tournament; thru 6 holes)

• • •

Hole No. 5, Par 4, 469 yards

Going last off the tee, Tiger sees Donald and McIlroy both miss the fairway with driver, so he pulls iron and puts it on the right side of the fairway.

From 196 yards, Tiger takes aim at the pin and flies over the flag and settles about 20 feet past the hole.

Donald has to simply punch down the fairway with his second shot, while McIlroy plays from a fairway bunker and lands in the same area as Tiger.

Tiger doesn’t play enough break on his birdie putt, but taps in safely for par.

Meanwhile, McIlroy picks up a second-straight birdie by rattling in a 12-footer. After taking three to get to the green, Donald two-putts and drops back to 1 under.

Tiger on the day: Even par (2 under for tournament; thru 5 holes)

• • •

Hole No. 4, Par 3, 174 yards

Coming off his first bogey of the week, Tiger safely puts it on the green and will have about 15 feet for birdie.

Donald comes up short of the green and lands in a greenside bunker while McIlroy tracks in much the same line as Tiger, but will have a bit further to go on his birdie putt.

Tiger two-putts for a par, Donald gets up-and-down to save par and McIlroy responds to his double-bogey on No. 3 with a birdie on No. 4.

Tiger on the day: Even par (2 under for tournament; thru 4 holes)

• • •

Hole No. 3, Par 4, 439 yards

All three players – Tiger, Donald and McIlroy – pull driver and all three hook it a bit too much and find fairway bunkers on the left side.

Tiger doesn’t play enough club out of the fairway bunker and comes up short and misses only his second green in regulation of the tournament, flying it into a greenside bunker. Looking to get up-and-down, his bunker shot runs to about eight feet under the hole. He misses the putt and picks up his first bogey of the tournament.

McIlroy flies the green and nearly hits a pocket of spectators with his second shot. He immediately lets go of his club on his third shot and it comes up well short of the green and in long rough. He makes a run at it with his chip, but it glides past and stops four feet away. He misses the putt and picks up double-bogey and is now 2 under (3 over for the day).

Donald is the only one to find the green with his shot out of the fairway bunker, and he two-putts for a par, nearly holing a 35-foot birdie effort.

Tiger on the day: Even par (2 under for the tournament; thru 3 holes)

Tiger Woods lines up a putt on Saturday, June 1, 1996, during the final round of the NCAA Men’s Golf Championships at The Honors Course in Ooltewah, Tenn. Woods went on to win the individual title. (AP Photo/Mark Humphrey)

This Nov. 10, 2010, file photo shows Tiger Woods at a news conference after his round at the Australian Masters Pro-Am event at Victoria Golf Club in Melbourne, Australia. Woods believes he finally is ready to move on after a self-destructive year that cost him his marriage, his mystique, millions in endorsements and, lastly, his No. 1 ranking. What remains are relationships to repair, along with his golf game.

Tiger Woods shakes hands with Jack Nicklaus after receiving the Jack Nicklaus College Player of the Year award in ceremonies at the Memorial Tournament in Dublin, Ohio, Sunday, June 2, 1996.

Tiger Woods holds his trophy aloft after winning the Las Vegas Invitational in Las Vegas, Nevada. It was the first win of his pro career.

Masters champion Tiger Woods holds a replica of the Masters Trophy after winning the tournament at the Augusta National Golf Club in Augusta, Ga., Sunday, April 13, 1997.

Tiger Woods celebrates as he wins the 1997 Masters with a record-breaking 18-under-par performance at the Augusta National Golf Club in Augusta, Ga., Sunday, April 13, 1997. (AP Photo/Curtis Compton)

Tiger Woods celebrates after winning the 100th U.S. Open Golf Championship at the Pebble Beach Golf Links in Pebble Beach, Calif., Sunday, June 18, 2000. Finishing at 12 under par, Woods topped second-place Ernie Els by a remarkable 15 shots.

Tiger Woods waves to fans after he won the 81st PGA Championship at the Medinah Country Club in Medinah, Ill., on Sunday, Aug. 15, 1999. Woods shot an 11-under 277, beating Sergio Garcia, of Spain, by one stroke. (AP Photo/Beth A. Keiser)

Tiger Woods, right, of the United States, holds the trophy as he makes his winner’s speech outside the clubhouse at the end of the final day of the British Open Golf championship on the Old Course at St. Andrews, Scotland, Sunday, July 23, 2000. At center is South Africa’s Ernie Els and at left Denmark’s Thomas Bjorn the joint second-place finishers. (AP Photo/Adam Butler)

In this Aug. 20, 2000 photo, Tiger Woods points to his ball as it drops for birdie on the first hole of a three-hole playoff against Bob May at the PGA Championship at Valhalla Golf Club in Louisville, Ky. (AP Photo/Chuck Burton, File)

Tiger Woods reacts on the 18th hole after winning the 2001 Masters by two strokes over David Duval at the Augusta National Golf Club in Augusta, Ga. The win was Woods’ fourth straight major title, completing what many would call the “Tiger Slam.”

Tiger Woods, left, receives the 2002 Masters Green Jacket from Augusta National Golf Club chairman William W. “Hootie” Johnson. The win was Woods’ third Masters title and second in a row.

Tiger Woods gestures as he watches his shot to the 13th hole Sunday, June 16, 2002 at the U.S. Open Golf Championship at the Black Course of Bethpage State Park in Farmingdale, N.Y. Woods went on to win by three shots over Phil Mickelson.

Tiger Woods, center, sits with his fiancee Elin Nordegren, left, and his friend Jerry Chang, right, during Stanford’s basketball game against Arizona in this Feb. 7, 2004.

Tiger Woods reacts to winning the 2005 Masters in a playoff with Chris DiMarco on the 18th hole during final-round play at Augusta National Golf Club in Augusta, Ga.

Tiger Woods speaks at a press conference with the trophy after winning the 2005 British Open on the Old Course at St. Andrews. (AP Photo/Ted S. Warren)

Tiger Woods, right, reacts as he walks off the 18th green with his caddie Steve Williams after winning the British Open Golf Championship at the Royal Liverpool Golf Course in Hoylake, England Sunday July 23, 2006. The win was Woods’ first major title since the death of his father, Earl.

Tiger Woods holds up the Wanamaker Trophy after winning the 89th PGA Golf Championship at the Southern Hills Country Club in Tulsa, Okla., Sunday, Aug. 12, 2007. The win was Tiger’s 13th major title.

Tiger Woods holds his left knee after teeing off on the second hole during the fourth round of the 2008 U.S. Open at Torrey Pines in San Diego. Woods had reconstructive surgery on his left knee Tuesday, June 24, 2008, in Utah to repair a torn ligament. Woods went on to win in a playoff over Rocco Mediate.

Tiger Woods reacts after sinking a birdie putt on the 18th green, forcing a playoff against Rocco Mediate during the final round of the 2008 U.S. Open at Torrey Pines in San Diego.

Phil Mickelson, left, winner of the Tour Championship and Tiger Woods, right, winner of the Fed Ex Cup, pose at East Lake Country Club.

Tiger Woods answered questions in a press conference Monday for the first time since his Thanksgiving night accident that led to revelations of multiple extramarital affairs.

Tiger Woods during the final round of the WGC-Bridgestone Invitational. On a Firestone Country Club course that he has dominated in the past, Woods posted his highest 72-hole score as a professional, including a closing 77 that left him in a tie for 78th place in the 79-man field.

Caddie Steve Williams holds a club as Tiger Woods hits on the driving range during a practice round for the PGA Championship.

Tiger Woods chats with the media after shooting 65 in the first round of The Barclays.

Tiger Woods doffs his cap after holing out for eagle on the 12th hole during Ryder Cup singles. In arguably his most dominant round of 2010, Woods claimed a 4-and-3 win over Francesco Molinari.

Tiger Woods of the U.S. and Steve Williams, caddie to Adam Scott, shake hands on the first tee during the Day 1 Foursome matches at the 2011 Presidents Cup

Tiger Woods of the U.S. celebrates with fans after the U.S. team defeated the International team on the final day of the Presidents Cup.

Tiger Woods celebrates after his birdie putt on the 18th hole to win the Chevron World Challenge.

Tiger Woods drops on No. 15 at Augusta National during the second round of the 2013 Masters. A day later, he was assessed a two-stroke penalty for an improper drop.

Tiger Woods won the Arnold Palmer Invitational on March 24 at Bay Hill Club & Lodge, Orlando, Fla. Earnings: $1,116,000

Tiger Woods after his seven-shot win in the 2013 WGC-Bridgestone Invitational in Akron, Ohio.

Tiger Woods (center right) and Rory McIlroy (centre left) walk side by side during their exhibition at Mission Hills.

Tiger Woods’ injury suffered on this swing Sunday has his PGA Championship and Ryder Cup status up in the air..

Tiger Woods flashes a smile on Sunday during the Hero World Challenge at Isleworth Country Club in Windermere, FL.

• • •

Hole No. 2, Par 5, 600 yards

Tiger pulls driver and gives it a wallop and the ball comes to rest in the first cut of rough on the right side of the fairway.

Donald finds the middle of the fairway with driver, while McIlroy joins Tiger in the first cut of rough.

Tiger chooses to lay up with his second shot, lofting a wedge in on his third shot, landing over the flag, about 15 feet from the hole. Tiger’s birdie putt has the right line, but stops short and Woods settles for another par on a par 5 (he parred all four of them on Thursday).

McIlroy gets inside of Tiger with his third shot, but misses a six-foot birdie putt and also cards a par.

Donald plays a brilliant third shot from the bunker to within five feet. He drains it and moves to 2 under for the tournament.

Tiger on the day: 1 under (3 under for tournament; thru 2 holes)

• • •

Hole No. 1, Par 4, 405 yards

Tiger, using long iron, drills it right into the center of the fairway, giving his normal “twirl” of the club in acceptance of the shot.

Donald finds the long rough off the tee, while McIlroy almost rolls through a fairway bunker, but the ball hits the lip and bounds back into the sand.

Tiger, decked out in all-white gear, goes right after the flag and lands about four feet from the pin and rolls to within six feet for birdie. He drains the putt and moves to 3 under.

Donald manages to hit the green from a tough spot in the rough, but will have more than 50 feet for birdie. He simply lag putts and settles for an opening two-putt par.

McIlroy has some bad luck with his second shot, taking it from a fairway bunker to a greenside bunker, where the ball buries and McIlroy has to simply blast out with his third shot, and the ball goes bounding by the hole and off the green. He chips to within a foot and picks up an opening bogey to fall back to 4 under.

Tiger for the day: 1 under (3 under for tournament; thru 1 hole)

• • •

Getting social with Golfweek

Look for European writer Alistair Tait on the scene, we will bring you shot-by-shot analysis of Tiger’s round on Thursday. Follow him on Twitter here, or Golfweek Magazine here.

• • •

Previewing Tiger’s debut

Tiger Woods finished 2011 in dramatic fashion, beating Zach Johnson to win the Chevron World Challenge and pick up his first win in more than two years.

Does that mean that Tiger is back? That we don’t know, but the signs point to a return to weekly contention.

We’ve spent a lot of time this week dissecting Tiger, including Jim McCabe’s feature story on where others feel that Tiger’s game is at and whether or not 2012 could be a return to old form. Check out that story here.

Our Alistair Tait also caught Tiger’s press conference on Tuesday, and left unimpressed, opining that Tiger needs to open up more about golf-centric questions. Read that story here.